Adaptive randomized range finder. \(\mathtt {RSVD}\)  is implemented based on the assumption that the target rank \(k\)  is know a priori. However, in practice, we may not know the true rank \(k\)  in advance. Therefore, it is desirable to design an algorithm that can find a matrix \(P\)  with as few orthonormal columns as possible such that
\(\left\Vert \left({I}-P P^{*}\right) A\right\Vert  \le \varepsilon \) 
where \(\varepsilon \)  denotes a given tolerance. The work in [1]}, based on results from [2]} describes an adaptive randomized ranger finder that iteratively samples until the desired tolerance is obtained. It is worth noting that the CPU time requirements of \(\mathtt {RSVD}\)  and the adaptive version are essentially identical.
